Fractures are analysed with the variational problem of energy functional and the boundary variational theorem of an arbitrary element for nonlinear solids is established, i.e.the equilibrium condition on the dynamics for the crack extension.

In this paper, using complex functional theory, the authors turn the potential flow around the surface irregulai ities in a pressure conduit and semi-infinite platforms into Dirichlet problem.

In this paper, the method of Block - Pulse Functions is used to directly slove the minimum value of energy, functional of bending beams, A new computer method for calculating deflection and slope of beams is proposd.

A new generalized variational principle in classical thin plate theory is proposed with deflection, transverse shear deformation, curvature, internal moment, transverse shearing force and unknown boundary reaction as argument functions. By applying slight restrictions to the argument functions, the new functional possesses the property of consecutive alternate max min.

The minimum value of the functional analysis of the energy in elastic compressed bars are directly solved by means of the properties of the block_pulse functions. A new numerical method for calculating the critical load of elastic compressed bars is obtained. This method is characterized by its convenience of calculation and computer processing.

The proof involves showing that a nonsymmetric version of the relevant integral is annihilated by a suitable ideal of the affine Hecke algebra, and that any such annihilated functional satisfies the desired vanishing property.

In this paper we analyze solutions of the n-scale functional equation Ф(x) = Σk∈?Pk Ф(nx-k), where n≥2 is an integer, the coefficients {Pk} are nonnegative and Σpk = 1.

Our main tool is a pointwise equality, relating a function f, and the associated functional g*(f), which has the form f2=h(f)+g*2(f), where h(f) is an explicit function.

The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant.

In Kolwankar and Lévy Véhel, new functional spaces, denoted $K^{s,s'}_{x_0}$, were

Local effects in the theory of elasticity are divided into two kinds in this paper. The one is induced by small rigidities and the other by small flexibilities. It is pointed out that these two kinds of local effects are essentially related to the principle of minimum potential energy and the principle of minimum complementary energy respectively. The main conclusion of this paper are as follows. When a problem of the theory of elasticity is formulated in variational principles, rigidities enter into the functional...

Local effects in the theory of elasticity are divided into two kinds in this paper. The one is induced by small rigidities and the other by small flexibilities. It is pointed out that these two kinds of local effects are essentially related to the principle of minimum potential energy and the principle of minimum complementary energy respectively. The main conclusion of this paper are as follows. When a problem of the theory of elasticity is formulated in variational principles, rigidities enter into the functional of potentially energy as parameters, and flexibilites enter into the functional of complementary energy as parameters. When one of these parameters approaches zero, the corresponding functional may degenerate such that the class of admissible functions is enlarged. When the solution of the degenerate problem consists of admissible functions of the original functional, there is no local effect. In this case, the solution of the original problem approaches uniformly to that of the degenerate problem as the parameter approaches zero. When the solution of the degenerate problem is not admissible in the original functional, there are some local effects.

This paper presents an approximate method to obtain the maximum residual deformation for impulsively loaded rigid-plastic structures. It is proved that the vanishing of the first variation of the functional J is equivalent to all the equations which should be satisfied in the dynamics of rigid-plastic continua. Under special conditions this generalized variational principle coincides with the previous two extremum principles[2,3]. We have applied our variational principle to the simply supported beam loaded...

This paper presents an approximate method to obtain the maximum residual deformation for impulsively loaded rigid-plastic structures. It is proved that the vanishing of the first variation of the functional J is equivalent to all the equations which should be satisfied in the dynamics of rigid-plastic continua. Under special conditions this generalized variational principle coincides with the previous two extremum principles[2,3]. We have applied our variational principle to the simply supported beam loaded by rectangular pulse and found that the results are much closer to the exact solution than those from the upper bound theorem[4] and lower bound theorem[5] in the rigid-plastic dynamics.

Variational principles of minimum potential energy and complementary energy of linear polar elasticity has been formulated by Nowacki [3 ]. As it has been proved by Chien Wei-zang, that the two generalized variational principles are equivalent in functional, wo now apply this important statement Chien's theorem, and Lagrange's method of multipliers to the establishing of generalized variational principle in polar elasticity for finite deformation. The fundamental equations of mechanics of finite deformation...

Variational principles of minimum potential energy and complementary energy of linear polar elasticity has been formulated by Nowacki [3 ]. As it has been proved by Chien Wei-zang, that the two generalized variational principles are equivalent in functional, wo now apply this important statement Chien's theorem, and Lagrange's method of multipliers to the establishing of generalized variational principle in polar elasticity for finite deformation. The fundamental equations of mechanics of finite deformation used are of which has been established in the author's paper [7], [4 ].